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	Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations
	Chen, Long ; Wang, Ming ; Zhong, Lin
	2015
英文摘要	In this paper, we consider the use of H(div) elements in the velocity?Cpressure formulation to discretize Stokes equations in two dimensions. We address the error estimate of the element pair (Formula Presented.), which is known to be suboptimal, and render the error estimate optimal by the symmetry of the grids and by the superconvergence result of Lagrange interpolant. By enlarging (Formula Presented.) such that it becomes a modified $$\mathrm{BDM}$$BDM-type element, we develop a new discretization (Formula Presented.). We, therefore, generalize the classical MAC scheme on rectangular grids to triangular grids and retain all the desirable properties of the MAC scheme: exact divergence-free, solver-friendly, and local conservation of physical quantities. Further, we prove that the proposed discretization (Formula Presented.) achieves the optimal convergence rate for both velocity and pressure on general quasi-uniform grids, and one and half order convergence rate for the vorticity and a recovered pressure. We demonstrate the validity of theories developed here by numerical experiments. ? 2014, Springer Science+Business Media New York.; SCI(E); EI; PubMed; 0; ARTICLE; chenlong@math.uci.edu; wangming.pku@gmail.com; lzhong1@uci.edu; 3; 716-744; 63
语种	英语
出处	EI
出版者	journal of scientific computing
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/263533]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chen, Long,Wang, Ming,Zhong, Lin. Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations. 2015-01-01.

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